South African Mathematics Olympiad First Round

Question

How many grams of pure gold must be added to five grams of a mixture that consists of 10% gold and 90% of some other metal so that the mixture will contain 20% gold? (A) 0.125 (B) 0.25 (C) 0.375 (D) 0.5 (E) 0.625

Accepted Answer

The initial 5 g of mixture contains 10% 5 = 0.5 g of gold. If we add x g of pure gold, then the mass of gold is (0.5 + x) g and the total mass is (5 + x) g. Therefore 0.5 + x = 20% (5 + x) = 1 + 0.2x, so 0.8x = 0.5 and x = 5/8 = 0.625.